GATE ME 2021 Set 1 — Question 50
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Manufacturing Processes → Forming → Rolling (Load & Torque)
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Question
A 200 mm wide plate having a thickness of 20 mm is fed through a rolling mill with two rolls. The radius of each roll is 300 mm. The plate thickness is to be reduced to 18 mm in one pass using a roll speed of 50 rpm. The strength coefficient () of the work material flow curve is 300 MPa and the strain hardening exponent, is 0.2. The coefficient of friction between the rolls and the plate is 0.1. If the friction is sufficient to permit the rolling operation then the roll force will be __________ KN (round off to the nearest integer).
Correct answer
775 to 784
Solution
Given:
Width of plate, mm
Initial thickness, mm
Final thickness, mm
Roll radius, mm
Roll speed, rpm
Strength coefficient, MPa
Strain hardening exponent,
Coefficient of friction,
mm
Since mm < mm, the friction is sufficient to permit the rolling operation.
MPa
(since MPa = N/mm)
Rounding off to the nearest integer, the roll force is KN.The final answer is
Width of plate, mm
Initial thickness, mm
Final thickness, mm
Roll radius, mm
Roll speed, rpm
Strength coefficient, MPa
Strain hardening exponent,
Coefficient of friction,
1.Calculate the draft () and average thickness ():
mmmm
2.Calculate the projected length of contact ():
mm3.Check if friction is sufficient for rolling:
Maximum possible draft mmSince mm < mm, the friction is sufficient to permit the rolling operation.
4.Calculate the true strain ():
5.Calculate the average flow stress ():
For a material with strain hardening, the average flow stress is given by:MPa
6.Calculate the roll force ():
The roll force is given by:(since MPa = N/mm)
7.Convert to KN and round off:
Rounding off to the nearest integer, the roll force is KN.The final answer is
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